Edge-Colorings of Graphs: A Progress Report
β Scribed by A. J. W. HILTON; ROBIN J. WILSON
- Book ID
- 119862772
- Publisher
- John Wiley and Sons
- Year
- 1989
- Tongue
- English
- Weight
- 413 KB
- Volume
- 576
- Category
- Article
- ISSN
- 0890-6564
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let x'(G), called the strong coloring number of G, denote the minimum number of colors for which there is a proper edge coloring of a graph G in which no two of its vertices is incident to edges colored with the same set of colors. It is shown that Z'~(G) ~< Fcn], Β½ < c ~ 1, whenever A(G) is appropr
## Abstract A proper coloring of the edges of a graph __G__ is called __acyclic__ if there is no 2βcolored cycle in __G__. The __acyclic edge chromatic number__ of __G__, denoted by __aβ²__(__G__), is the least number of colors in an acyclic edge coloring of __G__. For certain graphs __G__, __aβ²__(_
A k-forest is a forest in which the maximum degree is k. The k-arboricity denoted Ak(G) is the minimum number of k-forests whose union is the graph G. We show that if G is an m-degenerate graph of maximum degree A, then Ak(G) 5 [(A + (k -1) m -1)/k], k 2 2, and derive several consequences of this in
An edge-coloring of a graph G is equitable if, for each v β V (G), the number of edges colored with any one color incident with v differs from the number of edges colored with any other color incident with v by at most one. A new sufficient condition for equitable edge-colorings of simple graphs is